This paper investigates the momentum and contrarian investment strategies by Taiwan 50 index portfolio during the period of Apr. 2003 to Mar. 2006, and to verify the overreaction phenomenon exists or not, and compare the performances between these two strategies under the different investment formation and holding periods. After empirical studies, we find the performances of winner and loser portfolios are quite different in the 6, 12, and 18 months formation period under the fixed 12 months holding period. The average return of winner portfolio for 12 and 18 months are statistically significant higher than loser portfolio on 5% and 1% level, separately, but the average return between winner and loser portfolio for 6 months formation period are not statistically significant. Furthermore, in order to verify whether the performances of winner and loser portfolio are influenced by different time horizons, we extend the model to a three formation period × four holding period matrix, and find almost the average return of winner portfolio are statistically significant higher than the loser portfolio except in the component of 6 months formation period vs. 3 months holding period. These findings indicates the longer formation and holding period that investors do, the superior performances that momentum strategy does, and supports that the overreaction effect does not exist in Taiwan stock market.